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Appendix II.

which is the so-called equivalent twisting moment, although /e is
a direct stress and not a shear. The result is only true for round
shafts, but can be used for other sections by adopting proper
values of Z.

I :


P. 4^4-8.   Velocity  and Energy  Curves.     Let any

velocity curve, A, Fig. 823, be plotted to a base of equal times;
then  the  acceleration / will be   shewn   by  the   slope  curve

(see p. 852) of v, and v will be the sum curve of f, for velocity
growth v =//. Hence acceleration is rate of velocity change
regarding time. Again, at B, if an acceleration curve/be plotted
to equal distances, fd^^v* (for v* = 2/#). Therefore curve
^ #2 is the sum of f regarding ^, and the double of these
ordinates is #2, from which v may be found. Conversely, v being
known,/may be obtained directly, as on p. 492.

A curve of force at c will give an energy curve by summation,
for energy = p d. Many applications occur: thus, if / be an
indicator card, E will shew foot pounds (W^) given to piston, and